| Summary: | Many supermassive black holes (SMBH) of mass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mn>10</mn><mrow><mn>6</mn><mo>∼</mo><mn>9</mn></mrow></msup><msub><mi>M</mi><mo>⊙</mo></msub></mrow></semantics></math></inline-formula> are observed at the center of each galaxy even in the high redshift (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>≈</mo><mn>7</mn></mrow></semantics></math></inline-formula>) Universe. To explain the early formation and the common existence of SMBH, we previously proposed the SMBH formation scenario by the gravitational collapse of the coherent dark matter (DM) composed from the Bose-Einstein Condensed (BEC) objects. A difficult problem in this scenario is the inevitable angular momentum which prevents the collapse of BEC. To overcome this difficulty, in this paper, we consider the very early Universe when the BEC-DM acquires its proper angular momentum by the tidal torque mechanism. The balance of the density evolution and the acquisition of the angular momentum determines the mass of the SMBH as well as the mass ratio of BH and the surrounding dark halo (DH). This ratio is calculated as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>M</mi><mrow><mi>B</mi><mi>H</mi></mrow></msub><mo>/</mo><msub><mi>M</mi><mrow><mi>D</mi><mi>H</mi></mrow></msub><mo>≈</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn><mo>∼</mo><mo>−</mo><mn>5</mn></mrow></msup><msup><mrow><mo>(</mo><msub><mi>M</mi><mrow><mi>t</mi><mi>o</mi><mi>t</mi></mrow></msub><mo>/</mo><msup><mn>10</mn><mn>12</mn></msup><msub><mi mathvariant="normal">M</mi><mo>⊙</mo></msub><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula> assuming simple density profiles of the initial DM cloud. This result turns out to be consistent with the observations at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>≈</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>≈</mo><mn>6</mn></mrow></semantics></math></inline-formula>, although the data scatter is large. Thus, the angular momentum determines the separation of black and dark, i.e., SMBH and DH, in the original DM cloud.
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